Finite Group Databasebeta

← #11887360

Subgroups — #11887360

Order 1152.

630 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589714C211yesmaximal, characteristic, complemented
2#10589632C211yesmaximal, characteristic, complemented
3C9×#482C211yesmaximal, characteristic, complemented
4#10588721C211yesmaximal, characteristic, complemented
5#10588683C211yesmaximal, characteristic, complemented
6#10588564C211yesmaximal, characteristic, complemented
7#10588552C211yesmaximal, characteristic, complemented
8#10588551C211yesmaximal, characteristic, complemented
9#10588544C211yesmaximal, characteristic, complemented
10#10588467C211yesmaximal, characteristic, complemented
11#10588453C211yesmaximal, characteristic, complemented
12D9×#102C211yesmaximal, characteristic, complemented
13#10588448C211yesmaximal, characteristic, complemented
14#10588416C211yesmaximal, characteristic, complemented
15#611⋊C8C211yesmaximal, characteristic, complemented
16#81382—31nomaximal
17C2×D4×D9C2211yescharacteristic
18C2×#3697C2211yescharacteristic
19C9×#121C2211yescharacteristic
20C9×#117C2211yescharacteristic, complemented
21#63500—21no—
22#63499—21no—
23#63498C2211yescharacteristic
24C2×#3673C2211yescharacteristic
25#63492C2211yescharacteristic, complemented
26C4×#611C2211yescharacteristic
27C22×C9⋊C8C2211yescharacteristic, complemented
28C2×D72C2211yescharacteristic
29C2×#3664C2211yescharacteristic, complemented
30C2×C8×D9C2211yescharacteristic
31#63459C2211yescharacteristic
32#63457C2211yescharacteristic
33#63455C2211yescharacteristic
34#63455C2211yescharacteristic, complemented
35C4⋊C4×D9C2211yescharacteristic
36#63452C2211yescharacteristic, complemented
37#63446—21no—
38#63445—21no—
39#63445—21no—
40C22⋊C4×D9—21no—
41#63438—21no—
42C4×D36—21no—
43C9×#107C2211yescharacteristic, complemented
44C9×#106C2211yescharacteristic, complemented
45C9×#102C2211yescharacteristic
46C9×#102C2211yescharacteristic
47C9×C22⋊C8C2211yescharacteristic, complemented
48#63392C2211yescharacteristic
49#63380C2211yescharacteristic
50(C2×D9)⋊C8C2211yescharacteristic
51#63376C2211yescharacteristic, complemented
52Dic9⋊C8C2211yescharacteristic, complemented
53C8×Dic9C2211yescharacteristic, complemented
54#63369C2211yescharacteristic
55#63369C2211yescharacteristic
56#63369C2211yescharacteristic, complemented
57#63368C2211yescharacteristic, complemented
58#63368C2211yescharacteristic, complemented
59#63366C2211yescharacteristic, complemented
60#5612—31no—
61#5530—31no—
62C3×#482D311yescharacteristic
63#5038—31no—
64#5002—31no—
65#4884—31no—
66#4872—31no—
67#4871—31no—
68#4864—31no—
69#4787—31no—
70#4773—31no—
71D3×#102—31no—
72#4768—31no—
73#4734—31no—
74#67⋊C8—31no—
75C23×D9—21no—
76C2×D4×C9—21no—
77C2×D4×C9C2311yescharacteristic
78C22×C4×C9C2311yescharacteristic
79C2×#611—21no—
80C2×#611—21no—
81C2×#611—21no—
82C2×#611D411yescharacteristic
83D4×D9—22no—
84D4×D9—41no—
85#3697—22no—
86#3697—41no—
87C2×D36—21no—
88C2×D36C2311yescharacteristic
89C2×D36C2311yescharacteristic
90C2×C4×D9—21no—
91C2×C4×D9—21no—
92C2×C4×D9—21no—
93C2×C4×D9—21no—
94C2×C4×D9C2311yescharacteristic
95C2×Dic18C2311yescharacteristic
96C2×C8×C9C2311yescharacteristic
97C2×C8×C9C2311yescharacteristic
98C9×C4⋊C4C2311yescharacteristic
99C9×C4⋊C4C2311yescharacteristic
100C9×C4⋊C4C2311yescharacteristic
101C9×C22⋊C4—21no—
102C9×C22⋊C4—21no—
103C42×C9—21no—
104#3676—21no—
105#3676—21no—
106#3676D411yescharacteristic
107#3673—41no—
108(C2×D9)⋊C4—21no—
109(C2×D9)⋊C4—21no—
110(C2×D9)⋊C4—21no—
111(C2×D9)⋊C4—21no—
112(C2×D9)⋊C4—21no—
113(C2×D9)⋊C4D411yescharacteristic
114C4⋊Dic9—21no—
115C4⋊Dic9—21no—
116C4⋊Dic9C2311yescharacteristic
117Dic9⋊C4—21no—
118Dic9⋊C4—21no—
119Dic9⋊C4D411yescharacteristic
120C4×Dic9C2311yescharacteristic
121C2×C9⋊C8—41no—
122C2×C9⋊C8C2311yescharacteristic
123C2×C9⋊C8C2311yescharacteristic
124D72—22no—
125#3664—41no—
126C8×D9—41no—
127#3297—91noSylow
128C2×D3×D4—31no—
129C2×#235—31no—
130C3×#121C2×D311yescharacteristic
131C3×#117C2×D311yescharacteristic
132#938—61no—
133#937—61no—
134#936—31no—
135C2×#213—31no—
136#930—31no—
137C4×#67—31no—
138C22×C3⋊C8—31no—
139C2×D24—31no—
140C2×#204—31no—
141C2×D3×C8—31no—
142#897—31no—
143#895—31no—
144#893—31no—
145#893—31no—
146D3×C4⋊C4—31no—
147#890—31no—
148#884—61no—
149#883—61no—
150#883—61no—
151D3×C22⋊C4—61no—
152#876—61no—
153C4×D12—61no—
154C3×#107C2×D311yescharacteristic
155C3×#106C2×D311yescharacteristic
156C3×#102C2×D311yescharacteristic
157C3×#102C2×D311yescharacteristic
158C3×C22⋊C8C2×D311yescharacteristic
159#832—31no—
160#821—31no—
161(C2×D3)⋊C8—31no—
162#816—31no—
163Dic3⋊C8—31no—
164C8×Dic3—31no—
165#810—31no—
166#810—31no—
167#809—31no—
168#809—31no—
169#809—31no—
170#807—31no—
171C23×C9—21no—
172C23×C9C2×D411yescharacteristic
173C22×D9—21no—
174C22×D9—21no—
175C22×D9—42no—
176C22×D9—42no—
177C22×D9—81no—
178C22×D9C2×D411yescharacteristic
179D4×C9—21no—
180D4×C9—21no—
181D4×C9—81no—
182C2×C4×C9—21no—
183C2×C4×C9—21no—
184C2×C4×C9—21no—
185C2×C4×C9—21no—
186C2×C4×C9—21no—
187C2×C4×C9C2×D411yescharacteristic
188C2×C4×C9C2411yescharacteristic
189#611—22no—
190#611—42no—
191#611—42no—
192#611—81no—
193C2×Dic9—21no—
194C2×Dic9—21no—
195C2×Dic9C2×D411yescharacteristic
196C2×Dic9C2×D411yescharacteristic
197C2×Dic9C2×D411yescharacteristic
198D36—21no—
199D36—21no—
200D36—21no—
201D36—42no—
202D36#4112yes—
203C4×D9—21no—
204C4×D9—21no—
205C4×D9—42no—
206C4×D9—81no—
207C4×D9—81no—
208C4×D9—81no—
209Dic18—21no—
210Dic18—21no—
211C8×C9—21no—
212C8×C9—21no—
213C9⋊C8—21no—
214C9⋊C8—21no—
215#553—91no—
216#546—91no—
217#488—91no—
218#484—91no—
219#482D911yescharacteristic, complemented
220#478—91no—
221#466—91no—
222#465—91no—
223#463—91no—
224#449—91no—
225#447—91no—
226C4×D8—91no—
227C8×D4—91no—
228#416—91no—
229C2×#102—91no—
230C23×D3—61no—
231C2×C3×D4—21no—
232C2×C3×D4C22×D311yescharacteristic
233C22×C3×C4C22×D311yescharacteristic
234C2×#67—31no—
235C2×#67—61no—
236C2×#67—61no—
237C2×#67—61no—
238D3×D4—62no—
239D3×D4—121no—
240#235—62no—
241#235—121no—
242C2×D12—31no—
243C2×D12—31no—
244C2×D12—61no—
245C2×C4×D3—31no—
246C2×C4×D3—61no—
247C2×C4×D3—61no—
248C2×C4×D3—61no—
249C2×C4×D3—61no—
250C2×Dic6—31no—
251C2×C3×C8C22×D311yescharacteristic
252C2×C3×C8C22×D311yescharacteristic
253C3×C4⋊C4C22×D311yescharacteristic
254C3×C4⋊C4C22×D311yescharacteristic
255C3×C4⋊C4C22×D311yescharacteristic
256C3×C22⋊C4—21no—
257C3×C22⋊C4—21no—
258C3×C42—21no—
259#217—31no—
260#217—61no—
261#217—61no—
262#213—121no—
263(C2×D3)⋊C4—31no—
264(C2×D3)⋊C4—61no—
265(C2×D3)⋊C4—61no—
266(C2×D3)⋊C4—61no—
267(C2×D3)⋊C4—61no—
268(C2×D3)⋊C4—61no—
269C4⋊Dic3—31no—
270C4⋊Dic3—61no—
271C4⋊Dic3—61no—
272Dic3⋊C4—31no—
273Dic3⋊C4—61no—
274Dic3⋊C4—61no—
275C4×Dic3—31no—
276C2×C3⋊C8—31no—
277C2×C3⋊C8—31no—
278C2×C3⋊C8—121no—
279D24—62no—
280#204—121no—
281D3×C8—121no—
282C22×C9—21no—
283C22×C9—21no—
284C22×C9—21no—
285C22×C9—41no—
286C22×C9—41no—
287C22×C9—41no—
288C22×C9C22×D411yescharacteristic
289C2×D9—21no—
290C2×D9—21no—
291C2×D9—22no—
292C2×D9—41no—
293C2×D9—41no—
294C2×D9—41no—
295C2×D9—41no—
296C2×D9—41no—
297C2×D9—84no—
298C2×D9#13512yes—
299C4×C9—21no—
300C4×C9—41no—
301C4×C9—41no—
302C4×C9—41no—
303C4×C9C2×#4111yescharacteristic
304C4×C9H(5,𝔽2)11yescharacteristic
305Dic9—21no—
306Dic9—21no—
307Dic9—21no—
308Dic9—41no—
309Dic9—41no—
310C2×#41—91no—
311C22×D4—91no—
312C2×SD16—91no—
313C2×D8—91no—
314C2×D8—91no—
315C22×C8—91no—
316C22×C8—91no—
317#126—181no—
318#125—91no—
319#124—91no—
320#123—181no—
321#123—181no—
322C22⋊Q8—91no—
323#121—91no—
324#121—91no—
325#121—181no—
326#121—181no—
327#121C2×D911yescharacteristic
328#120—181no—
329C4×D4—91no—
330C4×D4—91no—
331C4×D4—91no—
332C4×D4—181no—
333#117C2×D911yescharacteristic, complemented
334C2×C4⋊C4—91no—
335C2×C22⋊C4—181no—
336#107—91no—
337#107C2×D911yescharacteristic, complemented
338#106C2×D911yescharacteristic, complemented
339C4⋊C8—91no—
340#103—91no—
341#103—91no—
342#103—91no—
343#102—91no—
344#102—91no—
345#102—91no—
346#102—91no—
347#102—91no—
348#102C2×D911yescharacteristic
349#102C2×D911yescharacteristic
350C22⋊C8—91no—
351C22⋊C8C2×D911yescharacteristic, complemented
352C4×C8—91no—
353C23×C3—21no—
354C23×C3D3×D411yescharacteristic
355C22×D3—31no—
356C22×D3—61no—
357C22×D3—61no—
358C22×D3—122no—
359C22×D3—122no—
360C22×D3—241no—
361C3×D4—21no—
362C3×D4—21no—
363C3×D4—81no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4C23×D311yescharacteristic
371#67—62no—
372#67—122no—
373#67—122no—
374#67—241no—
375C2×Dic3—31no—
376C2×Dic3—31no—
377C2×Dic3—31no—
378C2×Dic3—61no—
379C2×Dic3—61no—
380D12—32no—
381D12—61no—
382D12—61no—
383D12—61no—
384D12—122no—
385C4×D3—61no—
386C4×D3—61no—
387C4×D3—122no—
388C4×D3—241no—
389C4×D3—241no—
390C4×D3—241no—
391Dic6—61no—
392Dic6—61no—
393C3×C8—21no—
394C3×C8—21no—
395C3⋊C8—61no—
396C3⋊C8—61no—
397C2×C9—41no—
398C2×C9—81no—
399C2×C9#54611yescharacteristic
400C2×C9C2×#13511yescharacteristic
401C2×C9#57611yescharacteristic
402D9—22no—
403D9—42no—
404D9—81no—
405C24—181no—
406#41—182no—
407#41—361no—
408C2×Q8—91no—
409C2×D4—21no—
410C2×D4—91no—
411C2×D4—91no—
412C2×D4—91no—
413C2×D4—181no—
414C2×D4—181no—
415C2×D4—182no—
416C2×D4—181no—
417C2×D4—181no—
418C2×D4—361no—
419C2×D4C22×D911yescharacteristic
420C22×C4—91no—
421C22×C4—181no—
422C22×C4—181no—
423C22×C4—181no—
424C22×C4—181no—
425C22×C4C22×D911yescharacteristic
426SD16—361no—
427D8—182no—
428D8—361no—
429C2×C8—91no—
430C2×C8—91no—
431C2×C8—361no—
432C2×C8—361no—
433C2×C8C22×D911yescharacteristic
434C2×C8C22×D911yescharacteristic
435C4⋊C4—91no—
436C4⋊C4—91no—
437C4⋊C4—181no—
438C4⋊C4—181no—
439C4⋊C4—181no—
440C4⋊C4—181no—
441C4⋊C4C22×D911yescharacteristic
442C4⋊C4C22×D911yescharacteristic
443C4⋊C4C22×D911yescharacteristic
444C22⋊C4—21no—
445C22⋊C4—21no—
446C22⋊C4—91no—
447C22⋊C4—91no—
448C22⋊C4—181no—
449C22⋊C4—181no—
450C22⋊C4—181no—
451C22⋊C4—181no—
452C22⋊C4—181no—
453C22⋊C4—181no—
454C22⋊C4—181no—
455C42—21no—
456C42—91no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—21no—
460C22×C3—41no—
461C22×C3—41no—
462C22×C3—41no—
463C22×C3C2×D3×D411yescharacteristic
464C2×D3—32no—
465C2×D3—61no—
466C2×D3—61no—
467C2×D3—62no—
468C2×D3—121no—
469C2×D3—121no—
470C2×D3—121no—
471C2×D3—121no—
472C2×D3—121no—
473C2×D3—244no—
474C3×C4—21no—
475C3×C4—41no—
476C3×C4—41no—
477C3×C4—41no—
478C3×C4D3×#4111yescharacteristic
479C3×C4#100911yescharacteristic
480Dic3—61no—
481Dic3—61no—
482Dic3—61no—
483Dic3—121no—
484Dic3—121no—
485C9#329711yescharacteristic, complemented, Sylow
486C23—21no—
487C23—91no—
488C23—181no—
489C23—181no—
490C23—362no—
491C23—362no—
492C23—721no—
493C23D4×D911yescharacteristic
494Q8—181no—
495Q8—181no—
496D4—21no—
497D4—21no—
498D4—81no—
499D4—92no—
500D4—182no—
501D4—181no—
502D4—181no—
503D4—181no—
504D4—362no—
505D4—362no—
506D4—362no—
507D4—721no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—91no—
514C2×C4—91no—
515C2×C4—91no—
516C2×C4—181no—
517C2×C4—181no—
518C2×C4—181no—
519C2×C4—181no—
520C2×C4—362no—
521C2×C4—721no—
522C2×C4—721no—
523C2×C4—721no—
524C2×C4D4×D911yescharacteristic
525C2×C4C23×D911yescharacteristic
526C8—21no—
527C8—21no—
528C8—181no—
529C8—181no—
530C2×C3—41no—
531C2×C3—81no—
532C2×C3#565411yescharacteristic
533C2×C3D3×#13511yescharacteristic
534C2×C3#577411yescharacteristic
535D3—62no—
536D3—122no—
537D3—241no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—92no—
545C22—181no—
546C22—181no—
547C22—182no—
548C22—361no—
549C22—361no—
550C22—361no—
551C22—361no—
552C22—361no—
553C22—724no—
554C22C2×D4×D911yescharacteristic
555C4—21no—
556C4—41no—
557C4—41no—
558C4—41no—
559C4—181no—
560C4—181no—
561C4—181no—
562C4—361no—
563C4—361no—
564C4#41×D911yescharacteristic
565C4#6371511yescharacteristic
566C3#8138211yescharacteristic
567C2—41no—
568C2—81no—
569C2—182no—
570C2—362no—
571C2—721no—
572C2#1058975611yescharacteristic
573C2D9×#13511yescharacteristic
574C2#1058987611yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#482C2
socleC22×C3C2×D3×D4
hypercenter#482D9
hypocenterC9#3297
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #10589714C2semidirect
2. #10589632C2semidirect
3. C9×#482C2semidirect
4. #10588721C2semidirect
5. #10588683C2semidirect
6. #10588564C2semidirect
7. #10588552C2semidirect
8. #10588551C2semidirect
9. #10588544C2semidirect
10. #10588467C2semidirect
11. #10588453C2semidirect
12. D9×#102C2semidirect
13. #10588448C2semidirect
14. #10588416C2semidirect
15. #611⋊C8C2semidirect
20. C9×#117C22semidirect
25. #63492C22semidirect
27. C22×C9⋊C8C22semidirect
29. C2×#3664C22semidirect
34. #63455C22semidirect
36. #63452C22semidirect
43. C9×#107C22semidirect
44. C9×#106C22semidirect
47. C9×C22⋊C8C22semidirect
51. #63376C22semidirect
52. Dic9⋊C8C22semidirect
53. C8×Dic9C22semidirect
56. #63369C22semidirect
57. #63368C22semidirect
58. #63368C22semidirect
59. #63366C22semidirect
219. #482D9semidirect
333. #117C2×D9semidirect
337. #107C2×D9semidirect
338. #106C2×D9semidirect
351. C22⋊C8C2×D9semidirect
485. C9#3297semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#105897142
#105896322
C9×#4822
#105887212
#105886832
#105885642
#105885522
#105885512
#105885442
#105884672
#105884532
D9×#1022
#105884482
#105884162
#611⋊C82
#813823